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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.03244 |
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| _version_ | 1866917976537563136 |
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| author | Gao, Qinjiao Wang, Zuowei Zhang, Ran Wang, Dongjiang |
| author_facet | Gao, Qinjiao Wang, Zuowei Zhang, Ran Wang, Dongjiang |
| contents | In this paper, we propose the Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) to address challenges in solving nonlinear option pricing PDE models, where solutions often exhibit significant curvature or shock waves over time. The AM-PIRN architecture is designed to concurrently minimize PDE residuals and achieve high-fidelity option price approximations by dynamically redistributing training points based on evolving PDE residuals, while maintaining a fixed total number of points. To enhance stability and training efficiency, we integrate a ResNet backbone, replacing conventional fully connected neural networks used in Physics-Informed Neural Networks (PINNs). Numerical experiments across nonlinear option pricing models demonstrate that AM-PIRN outperforms PINN, RAM-PINN, and WAM-PINN in both resolving PDE constraints and accurately estimating option prices. The method's advantages are particularly pronounced in complex or multi-dimensional models, where its adaptive sampling and robust architecture effectively mitigate challenges posed by sharp gradients and high nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03244 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models Gao, Qinjiao Wang, Zuowei Zhang, Ran Wang, Dongjiang Networking and Internet Architecture In this paper, we propose the Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) to address challenges in solving nonlinear option pricing PDE models, where solutions often exhibit significant curvature or shock waves over time. The AM-PIRN architecture is designed to concurrently minimize PDE residuals and achieve high-fidelity option price approximations by dynamically redistributing training points based on evolving PDE residuals, while maintaining a fixed total number of points. To enhance stability and training efficiency, we integrate a ResNet backbone, replacing conventional fully connected neural networks used in Physics-Informed Neural Networks (PINNs). Numerical experiments across nonlinear option pricing models demonstrate that AM-PIRN outperforms PINN, RAM-PINN, and WAM-PINN in both resolving PDE constraints and accurately estimating option prices. The method's advantages are particularly pronounced in complex or multi-dimensional models, where its adaptive sampling and robust architecture effectively mitigate challenges posed by sharp gradients and high nonlinearity. |
| title | Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models |
| topic | Networking and Internet Architecture |
| url | https://arxiv.org/abs/2504.03244 |